Question

if cos(a+b)=0 then sin(a-b) can be reduced to what
a) cos b
b)cos 2b
c) sin a
d)sin 2a
and give reason why???

Answer 1

cos 2b
is the answer
hope it helps

Answer 2

Answer:

Option B is correct.

Step-by-step explanation:

Given that cos(a+b)=0

then we have to find the reduced form of sin(a-b)

As, $cos(a+b)=0$

⇒ $a+b=cos^{-1}(0)=90^{\circ}$

⇒ $a=(90-b)^{\circ}$

$sin(a-b)=sin(90-b-b)=sin(90-2b)=cos{2b}$

Hence, sin(a-b)=cos{2b}

∴ option b) is correct.